Natural principal connections on the principal gauge prolongation of a principal bundle

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Title in English Natural principal connections on the principal gauge prolongation of a principal bundle
Authors

JANYŠKA Josef VONDRA Jan

Year of publication 2009
Type Article in Periodical
Magazine / Source REPORTS ON MATHEMATICAL PHYSICS
MU Faculty or unit

Faculty of Science

Citation
Web http://www.elsevier.com/wps/find/journaldescription.cws_home/416/description#description
Field General mathematics
Keywords natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection
Description Let $\Gamma$ be a principal connection on a principal bundle $\pi:P\to M$ and let $\Lambda$ be a linear connection on $M$. We describe all possible natural prolongations of $\Gam$, with respect to $\Lam$, to principal connections on the principal gauge prolongation $W^rP$ of $P$. For $r=1,2$ we give the full classification, for $r\ge 3$ we give a base of natural operators which generates all possible natural principal connections on $W^rP$.
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